Question

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red

Answer 1

Out of 16 balls, two balls can be drawn in ¹⁶C₂ ways.
∴ Total number of elementary events = ¹⁶C₂ = 120

Out of five black balls, one black ball can be drawn in ⁵C₁ ways.
Out of four red balls, one red ball can be drawn in ⁴C₁ ways.
 Therefore, one black and one red balls can be drawn in ⁵C₁× ⁴C₁ ways.
∴ Favourable number of ways = ⁵C₁× ⁴C₁ = 5× 4 = 20
Hence, required probability = \[\frac{20}{120} = \frac{1}{6}\]